Best Known (29, 59, s)-Nets in Base 8
(29, 59, 74)-Net over F8 — Constructive and digital
Digital (29, 59, 74)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 15, 9)-net over F8, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (14, 44, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (0, 15, 9)-net over F8, using
(29, 59, 76)-Net in Base 8 — Constructive
(29, 59, 76)-net in base 8, using
- 1 times m-reduction [i] based on (29, 60, 76)-net in base 8, using
- base change [i] based on digital (5, 36, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- base change [i] based on digital (5, 36, 76)-net over F32, using
(29, 59, 109)-Net over F8 — Digital
Digital (29, 59, 109)-net over F8, using
(29, 59, 3262)-Net in Base 8 — Upper bound on s
There is no (29, 59, 3263)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 191619 074964 858755 917901 012257 971335 955075 769519 786136 > 859 [i]